GEEKSPEAK

GEEKSPEAK

How Life + Mathematics = Happiness

Dr Graham Tattersall

This book is written in memory of my father, who helped raise six children as well as quietly going through life inventing, analysing, and mending anything and everything.

PHOTOGRAPH
ACKNOWLEDGEMENTS

All photos, unless stated, taken from Stock.XCHNG.com.

Introduction: Living with Numbers: #347053, Aleksander Milosevic, Belgrade, Serbia

1 Scrabbling for Words: #650192, Steve Woods/Pinpoint, Essex, UK

2 Pumping Iron: #313419, Josef Lluis Caldentey, Spain

3 Safe as Houses: Author

4 Well Connected: #368906, Cory McKenzie, Canada

5 Fatal Attraction: #696930, Marcos Santos, Brazil

6 Home Alone: #656412, Liv Crazy, Australia

7 Beam Me Up, Scotty: #757924, Artiom, Ukraine (StockExpert)

8 Hidden Death: #97469, Ken Kiser, US

9 It’s For You: #6926, Stephen Gibson/ BudgetStockPhoto.com, Australia

10 War Chest: #522105, Marcin Barlowski, Poland

11 When the Wind Blows: #739813, George Bosela, US

12 You’re Rubbish: #315128, Liton Ali, London, UK

13  Nappy Crap: #560650, Pascal Montsma, Netherlands

14 The Cunning Fox: #769992, Lynne Lancaster (weirdvis), UK

15 Fly Wheels: #735390, Asif Akbar, India

16 Bus Stop: #198141, Tomasz Kowalczyk, Poland

17 Stirring Airs: #442256, Steve Ford Elliot, Eire

18 Dream Flight: #748302, Martin Brooks, UK

19 Processing Power: #370098, Max Brown, Sydney, Australia

20 Soul Mates: #264203, Paul Preacher, London, UK

21 Idiot Calculus: #282161, Anka Draganski, London, UK

22 The Ghostly Present: #708887, Robert Rosmond, New Orleans, US

23 Bad Breath: #398156, Tudou Mao, Shijiazhuang, China

24 Wave Power: Author

25 Mechanical Neurosis: #242268, Philippe Ramakers, Belgium

26 The Final Judgement: #19734, alxm (StockExpert)

27 Heavenly Body: #707105, Wojtek Wozniak, Zabrze, Poland

28 Passing Water: #633517, Emin Ozkan, Zmin, Turkey

29 The Man in White: #700514, Joan Koele, Netherlands

GEEKSPEAK

INTRODUCTION

LIVING WITH

NUMBERS

How Much can you work out about your own world?

For as long as I can remember, I’ve been fascinated by how things work. There’s a whole world of cogs, circuit boards and equations behind familiar objects and events, or the figures and statistics we see in the media. I can pinpoint the exact moment when this fascination was born: it was as an eight-year-old child on a family trip to the Scottish Highlands. Frantically looking for a way to distract his squabbling children, my father announced that ‘The first person to tell me the weight of that mountain gets to sit in the front of the car.’ I took on the task, excitedly shouting out wrong answers.

This was power – working out a new number, a new piece of knowledge about the world that hadn’t existed ten seconds earlier. And, it happened in a person’s head. It was amazing.

And that was it: I became a Geek.

A family friend dropped by after our return. He was an amateur radio enthusiast, and his car was festooned with all sorts of antennas. ‘Watch this,’ he said through a large smile, and placed his finger at the bottom end of an antenna.

The faint, sweet smell of burning flesh drifted towards me as the current from the antenna flowed through his skin, heating and burning its extreme outer surface, but without the strength to cause any pain or real damage.

I was transfixed. How had that happened? Why hadn’t it hurt? How deep had the current penetrated? And, was it possible to work out how much energy had been spent in his finger? Here were more questions, more knowledge to attain, more facts and figures, all calculable inside a person’s head.

The fascination with the simple conjuror’s trick of the burning skin has stayed with me, as a desire to explore the hows and whys lurking behind everyday life. And that, in a nutshell, is what this book is about: how to analyse your world and come up with your own new knowledge and understanding.

But perhaps most importantly, it’s about your ability to judge and check ‘expert’ opinion for yourself rather than take it as granted – about using your numeracy to be better informed in debates about our shared future.

Have a look at a couple of ‘expert’ assertions. Do you believe them? How would you judge their validity?

Britain should focus on the development of wind and wave power to meet its electricity generation needs.

Hormone replacement therapy (HRT) greatly increases the risk of breast cancer.

Neither statement can be tested without using some numbers: the amount of power that can be generated by a wind turbine, and the electricity needed to run Britain; and the statistical significance and experimental controls used to make the HRT assertion.

But the numbers themselves are of little value. For a more complete knowledge of the issues, the assumptions, caveats and uncertainties in their calculation need to be understood. And the only way to understand all those is to do the calculation yourself.

Many people think that to perform that kind of calculation you need to be an expert in the given field – which is why we tend to rely on experts. You might go along with that, and decide that it’s best to leave it to the professionals, the politicians and the people in white coats.

But there is another way: a path of knowledge, learning and understanding – the way of the Geek. Not an obsessive, narrow-interest, malodorous Geek, but a nice, thoughtful, sweet-smelling Geek, the kind you’d like as a friend.

A true Geek can get at the truth by understanding the limits of a calculation, by knowing when to approximate 3.783 million as ‘about 4 million’. A true Geek knows how to simplify the analysis so that the answer, though not spot on, will still be accurate enough to guide opinion.

Oh, and a true Geek is interested in the mathematics of body size, and of God, sex, food and a whole load of other things that also interest quite normal people.

And this is the rub. We live surrounded by figures: the power of a wind turbine, the amount the average family spends on food, the fuel consumption of a Boeing 747, the weight of sewage you create each year. Not being able to estimate such figures yourself – not speaking any Geek – is like living in a foreign country and not being able to communicate.

How can you trust statements made by academics, architects, scientists and politicians without checking the underlying numbers?

You can’t!

But you can work it out for yourself. And what’s more, once you’ve done that it’s better than just knowing the fact. You’ll understand the basis and limits of its truth.

So this book is about empowerment, by combining common sense, straightforward arithmetic and a little questioning of received wisdom.

This book shows you how to speak Geek.

1

SCRABBLING
FOR WORDS

How big is your vocabulary?

You know thousands of words with many different meanings. Jane Austen uses over 6,000 different words in Pride and Prejudice, and you can read them all without the slightest problem. In fact, your passive reading vocabulary probably exceeds 10,000 words. Can you remember the last time you heard or read a word whose meaning you didn’t know?

On the other hand, your active vocabulary – the words you use in everyday speech – will be much more limited. On an average day you’ll probably get by on a few hundred words. And those words say a lot about you: your sex, age and social class.

In the early 1990s, recordings were made of conversations and used to build a database of words in the English language. The database, held at the University of Lancaster, contains over 100 million words spoken by men and women of all ages and occupations. Some interesting facts were pulled out of this data by three researchers, Paul Rayson, Geoffrey Leech and Mary Hodges. One of the most startling is the difference between the kind of words used by men and those used by women. It turned out that there are certain words which act like fingerprints, showing that a conversation is between two men, or between two women.

These are the top three fingerprint words in women’s conversation:

she

her

said

And the three words most characteristic of man-to-man conversation:

fucking

er

the

Those top three female words are instantly recognisable as typical of ‘girl talk’. Just eavesdrop on a conversation between two women chatting near the office coffee machine: ‘And she said that her friend was really upset… And I said to her…’

As for the men, here are a couple of guys leaning over the open bonnet of a car: ‘What’s that fucking wire doing?’ ‘Er, dunno. The battery’s dead.’

Similar studies reveal words that distinguish social groups. Words such as ‘actually’ and ‘really’ are indicative of Groups A, B and C1; ‘bloke’, ‘bloody’ and ‘pound’ are distinctly C2, D and E.

The journey from the equality of baby burbling to speaking in ways that encode your gender, age and social status takes two or three decades, but you can go back to the first moments after your birth quite easily. Start by letting every muscle in your mouth and lips go slack. Now make a noise.

That grunt is called the schwa. It is the most basic, neutral vowel sound, and sounds similar, though not identical, when uttered by people with different mother tongues.

In the first few months after your birth, you’ll start to babble, and by the time you’re coming up to your first birthday you’ll have a few words. Those words use vowel sounds such as u as in ‘mum’ and a as in ‘man’. They’ll be bracketed by primitive consonants or nasal sounds such as m and n to create important words such as ‘mumma’ and ‘dadda’.

Fast-forward to the age of around eighteen months, and you’ll be making much more complex sounds by articulating most vowels and consonants, and introducing l and n sounds.

The extremes of the vowel sounds are the cardinal points of your language. In English, they range from a as in ‘cat’ and i as in ‘hit’, to oo as in ‘hoot’ and aw as in ‘saw’. You can utter a kind of sound circle with the cardinal vowels. Voice them in sequence and you’ll find that the sound changes smoothly from one vowel to the next.

Counting vowels, consonants, nasals, and l and r sounds, a fully developed English speaker can recognise at least forty-five basic sounds. They are called phonemes.

It used to be thought that each phoneme was a distinct acoustic event, but it is now accepted that many are psycho-perceptual. For example, the stop consonant pp in the word ‘apple’ does not exist by itself. A stop consonant is the sound we think we hear ourselves saying when we use our mouth to rapidly stop or start a sound. The pp in ‘apple’ is the sound made when we quickly close our lips to stop making the a sound, and then explosively open them again to continue with the le sound.

We perceive the stop consonant as an actual sound that exists between the a and the le. But if you look at the sound trace of someone saying ‘apple’, you’ll see a period of silence in the middle of the word. That’s the pp in ‘apple’. It doesn’t exist: it’s simply perceived because of the way the a and le are stopped and started.

One of the drawbacks of growing up speaking your mother tongue is losing responsiveness to speech sounds in other languages. This was demonstrated by Japanese researchers. They played sounds to infants while monitoring the frequency with which the infants sucked on a dummy. They sucked more often when there was a recognisable stimulus such as their mother’s face or a familiar sound.

Newborns, who had barely been exposed to their mother tongue, sucked rapidly when they heard any of a wide variety of sounds drawn from many languages. Older infants sucked rapidly only when they heard sounds used in their mother tongue. The researchers inferred that infants lose the ability to distinguish certain sounds when they start to learn a language in which those sounds are absent.

Now, hopefully many years after you stopped sucking because something seemed familiar, you understand, speak and read thousands of words. It’s rather strange that we bother, when just a few hundred words are sufficient for our daily lives.

So, how many words do you know?

It’s possible to work out the size of your passive vocabulary. One approach is to go through every entry in a dictionary and tick off every word you know. But if you’ve got other things to do in life, there’s a smarter way that gives a good estimate in a much shorter time. That method is called statistical sampling.

The idea behind statistical sampling is the same as used in surveys of, for example, voters. The nation’s intended voting pattern could be found by asking all 30 million voters about their plans for the voting booth. More practically, a representative sample of voters is questioned. The sample might consist of just 1,000 people carefully selected to represent all the localities and social groups in the country.

The same approach can be used to estimate your vocabulary. Sample the ‘population’ of words by opening the dictionary at random 100 times. Each time, look at the first entry at the top of the page. Do you know the meaning of this word? If the answer is yes, add one to your word score. At the end of the exercise, divide your score by the sample size of one hundred to get an estimate of the fraction of words in the dictionary that you know. Multiply that fraction by the total number of words in the dictionary to make an estimate of your vocabulary size.

This method works, but you need to be careful: how many times should you dip into the dictionary at random to get a good estimate? Say you do the test twice and find that you know the first word, but not the second. That means that you know 50% of the words in the tiny bit of the dictionary you examined.

But common sense tells you that this estimate is unreliable. It is true that you might know half the dictionary, but it is also possible that you know 10% or 90% of all the words. The two words you chanced upon might have been unusually uncommon, or unusually common. Two out of however many thousand words the dictionary defines is not a representative sample.

Do the trial 10 times, and confidence in the result is greater; 100 times, even better. If you did the trial 1,000 times and found that you knew 500 words, you could argue quite strongly that you really do know about half of all the words in the dictionary.

To complete the estimate of your vocabulary you’ll need to know the total number of words in the dictionary – preferably without having to count them. This is quite easy: look up the number of the last page in the dictionary, and take that as the number of pages. Next, open the dictionary at random and count the number of different words listed on that page. Multiply the number of pages by the number of words per page, and you have an estimate of the number of words in the dictionary.

I thought I’d better test myself using this statistical sampling technique. The dictionary I used has about 60 entries on each page, and over 800 pages. That’s around 48,000 words altogether.

I opened the dictionary 125 times, and made a tick on a piece of paper if I knew the meaning of the word at the top of the page, and a cross if I didn’t. Like me, you’ll probably find it hard to stop yourself jumping ahead to other entries if the first is unfamiliar. Don’t – that’s cheating, and invalidates the statistical sampling!

The result: there were 25 words whose meaning I didn’t know. On that basis, my passive vocabulary is 48,000 multiplied by 100/125. That’s around 40,000 words. It sounds high, but it includes all the possible extensions of the stem of each word. For example, take the word ‘abstract’. The dictionary will include ‘abstractedly’, ‘abstractedness’, and so on. The number of stem words I know is a lot less than 40,000.

Still, I’m feeling pretty good about myself, so I’m going to exercise my gigantic male vocabulary by introducing the next chapter:

‘The, er, next chapter is, er, fucking interesting…’

SPEAK GEEK

‘IT IS A TRUTH UNIVERSALLY ACKNOWLEDGED THAT A SINGLE MAN IN POSSESSION OF A GOOD FORTUNE MUST BE IN WANT OF A WIFE.’

Some authors are instantly recognisable from their vocabulary. For example, everyone recognises the style of Jane Austen, and many would say that her writing’s distinguishing feature is its abundance of long words. But is this true? A bit of statistical analysis can reveal the answer.

The four longest words used by Jane Austen in Pride and Prejudice have 16 or 17 characters. They are ‘superciliousness’, ‘communicativeness’, ‘disinterestedness’ and ‘misrepresentation’. But just looking at the longest words is not enough: we need to examine the distribution of word lengths over her entire vocabulary, as shown in the graph below:

For comparison, here is the ‘fingerprint’ of the writer Ian McEwan, showing that his vocabulary includes many shorter words:

And, what about this book? In this work I intend to speak with candour, and without misrepresentation or superciliousness, of the accomplishments of the irreproachable retrospections…

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